On the effect of estimating the error density in nonparametric deconvolution

Neumann, Michael H.; Hössjer, Ola

doi:10.1080/10485259708832708

Cited by 121 publications

(167 citation statements)

References 19 publications

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“…In the first papers, the noise distribution is assumed to be known, see [29] for nonadaptive kernel, [57] for adaptive wavelet estimator and [22] for adaptive cut-off selection. More recently, the case of unknown noise distribution has been considered, see [55], [41], [21], [44]. The estimation of the Lévy density for Lévy processes relies on the explicit form of the characteristic function and thus takes inspiration in the deconvolution methods.…”

Section: Bibliographic Commentsmentioning

confidence: 99%

Adaptive Estimation for Lévy Processes

Comte

Genon-Catalot

2014

Lévy Matters IV

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Section: Bibliographic Commentsmentioning

confidence: 99%

Adaptive Estimation for Lévy Processes

Comte

Genon-Catalot

2014

Lévy Matters IV

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“…The error induced by the truncation is studied in the following lemma, which is an extension of Neumann [1997]'s lemma for the case we study here. (1) There exists a constant C 0 such that…”

Section: Estimators With Unknown Noise Densitymentioning

confidence: 99%

“…Then several extensions have been considered to relax the assumption about noise density knowledge. Neumann [1997] first studied the case where the noise density is estimated from a preliminary noise sample. A complete adaptive procedure has been provided by Comte and Lacour [2011].…”

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confidence: 99%

Nonparametric estimation of random-effects densities in linear mixed-effects model

Comte

Samson

2012

Journal of Nonparametric Statistics

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Abstract. We consider a linear mixed-effects model where Y k,j = α k +β k tj +ε k,j is the observed value for individual k at time tj, k = 1, . . . , N , j = 1, . . . , J. The random effects α k , β k are independent identically distributed random variables with unknown densities fα and f β and are independent of the noise. We develop nonparametric estimators of these two densities, which involve a cutoff parameter. We study their mean integrated square risk and propose cutoff-selection strategies, depending on the noise distribution assumptions. Lastly, in the particular case of fixed interval between times tj, we show that a completely data driven strategy can be implemented without any knowledge on the noise density. Intensive simulation experiments illustrate the method.

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“…For the remaining term in (4), we write first: Neumann (1997) proved that there exists a positive constant C 1 such that…”

Section: Proof Of Proposition 31mentioning

confidence: 99%

Pointwise deconvolution with unknown error distribution

Comte

Lacour

2010

Comptes Rendus. Mathématique

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This note presents rates of convergence for the pointwise mean squared error in the deconvolution problem with estimated characteristic function of the errors. RésuméDéconvolution ponctuelle avec distribution de l'erreur inconnue. Cette note présente les vitesses de convergence pour le risque quadratique ponctuel dans le problème de déconvolution avec fonction caractéristique des erreurs estimée.

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On the effect of estimating the error density in nonparametric deconvolution

Cited by 121 publications

References 19 publications

Adaptive Estimation for Lévy Processes

Adaptive Estimation for Lévy Processes

Nonparametric estimation of random-effects densities in linear mixed-effects model

Pointwise deconvolution with unknown error distribution

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